Paul, a tea party leader in Congress, is backing businessman Greg Sowards, who has an uphill climb against former Rep. Heather Wilson in the June 5 GOP contest.

"I’m calling on conservatives, libertarians, and Tea Party activists in New Mexico and across the nation to support Greg Sowards,” Paul said in a statement. “He will stand for the Constitution and I’m proud to stand with him."

A poll conducted for Wilson in February found her leading Sowards 81 percent to 10 percent. Through March 31, Sowards had $706,000 in cash on hand — about half that of Wilson — thanks largely to loaning his campaign more than $1.1 million. Sowards raised less than $5,000 from individual donors last quarter.

Wilson has not seen the kind of third-party group involvement against her that occurred in 2008, when hundreds of thousands of dollars poured into the state to upend her first Senate bid against Rep. Steve Pearce, who went on to lose in the general election to now-Sen. Tom Udall (D).

Paul said Sowards supports a five-year balanced budget that he and GOP Sens. Jim DeMint (S.C.) and Mike Lee (Utah) proposed. "He agrees that our future generations of Americans do not deserve to be enslaved by debt, and we need more champions like him in the U.S. Senate," Paul said.

The winner will take on either Rep. Martin Heinrich or state Auditor Hector Balderas, who are vying for the Democratic nomination, in what's likely to be a competitive general election. The Senate seat opened with the retirement of Sen. Jeff Bingaman (D).